Clustering on Multi-Layer Graphs via Subspace Analysis on Grassmann Manifolds

Relationships between entities in datasets are often of multiple types, which can naturally be modeled by a multi-layer graph; a common vertex set represents the entities and the edges on different layers capture different types of relationships between the entities. In this paper, we address the problem of analyzing multi-layer graphs and propose methods for clustering the vertices by efficiently merging the information provided by the multiple modalities. We propose to combine the characteristics of individual graph layers using tools from subspace analysis on a Grassmann manifold. The resulting combination can then be viewed as a low dimensional representation of the original data which preserves the most important information from diverse types of relationships between entities. We use this information in new clustering methods and test our algorithm on several synthetic and real world datasets to demonstrate its efficiency.